A classification of unimodular lattice wiretap codes in small dimensions

IEEE Transactions on Information Theory

Volumn 59, Issue 6, 2013, Pages 3295-3303

  Lin, Fuchun ^a   Oggier, Frederique ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Gaussian channel; lattice codes; secrecy gain; theta series; unimodular lattices; wiretap codes

Indexed keywords

GAUSSIAN CHANNELS; LATTICE CODES; SECRECY GAIN; THETA SERIES; UNIMODULAR; WIRETAP CODES;

COMPUTER APPLICATIONS; INFORMATION THEORY;

TELECOMMUNICATION;

EID: 84877902869     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2013.2246814     Document Type: Article

References (18)

1. J.-C. Belfiore and F. Oggier, "Secrecy Gain: A Wiretap Lattice Code Design," in Proc. ISITA, 2010 [Online]. Available: http://arXiv:1004. 4075v2 [cs.IT]
2. A. D.Wyner, "The wire-tap channel," Bell. Syst. Tech. J., vol. 54, Oct. 1975.
3. Y. Liang, H. V. Poor, and S. Shamai, "Information theoretic security," Found. Trends Commun. Inf. Theory, vol. 5, no. 4-5, pp. 355-580, 2009.
4. L. H. Ozarow and A. D.Wyner, "Wire-tap channel II," Bell Syst. Tech. J., vol. 63, no. 10, pp. 2135-2157, Dec. 1984.
5. A. Thangaraj, S. Dihidar, A. R. Calderbank, S. W. McLaughlin, and J.-M. Merolla, "Applications of LDPC codes to the wiretap channel," IEEE Trans. Inf. Theory, vol. 53, no. 8, pp. 2933-2945, Aug. 2007. (Pubitemid 47249863)
6. S. K. Leung-Yan-Cheong and M. E. Hellman, "The Gaussian wire-tap channel," IEEE Trans. Inf. Theory, vol. IT-24, no. 4, pp. 451-456, Jul. 1978.
7. D. Klinc, J.Ha, S. McLaughlin, J. Barros, and B. Kwak, "LDPC codes for the Gaussian wiretap channel," in Proc. IEEE Inf. Theory Workshop, Oct. 2009, pp. 95-99.
8. R. Liu, H. V. Poor, P. Spasojevic, and Y. Liang, "Nested codes for secure transmission," in Proc. IEEE Pers. Indoor Mobile Radio Conf., 2008, pp. 1-5.
9. J.-C. Belfiore and P. Solé, "Unimodular lattices for the Gaussian wiretap channel," presented at the IEEE Inf. TheoryWorkshop, Dublin, Ireland, 2010 [Online]. Available: [cs.IT]
10. F. Oggier, J.-C. Belfiore, and P. Solé, Lattice coding for the wiretap Gaussian channelMar. 21, 2011 [Online].Available: http://arXiv:1103. 4086v1 [cs.IT]
11. A.-M. Ernvall-Hytönen, "On a Conjecture by Belfiore and Solé on some Lattices," IEEE Trans. Inf. Theory., to be published.
12. A.-M. Ernvall-Hytönen and C. Hollanti, "On the Eavesdropper's correct decision in Gaussian and fading wiretap channels using lattice codes," in Proc. IEEE Inf. Theory Workshop, Paraty, Brazil, 2011, pp. 210-214.
13. W. Ebeling, "Lattices and codes," in Advanced Lectures in Mathematics. Braunschweig/Wiesbaden, Germany: Verlagsgesellschaft mbH, 1994.
14. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 3rd ed. New York, NY, USA: Springer-Verlag, 1998.
15. N. Koblitz, Introduction to Elliptic Curves and Modular Forms, ser. Graduate Texts in Math No. 97, 2nd ed. New York, NY, USA: Springer-Verlag, 1993.
16. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North Holland, 1977.
17. [Online]. Available: http://www.cs.umanitoba.ca/umbilou1/SelfDual-Codes/ toc.html
18. F. Lin and F. Oggier, "Secrecy gain of Gaussian wiretap codes from unimodular lattices," in Proc. Inf. Theory Workshop, Paraty, Brazil, 2011, pp. 718-722.